William is 24 years older than Kevin. Thirteen years ago, William was 4 times as old as Kevin. How old is Kevin now?
Solution: We can use the given information to write down two equations that describe the ages of William and Kevin. Let William's current age be $w$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $w = k + 24$ Thirteen years ago, William was $w - 13$ years old, and Kevin was $k - 13$ years old. The information in the second sentence can be expressed in the following equation: $w - 13 = 4(k - 13)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to use our first equation for $w$ and substitute it into our second equation. Our first equation is: $w = k + 24$ . Substituting this into our second equation, we get the equation: $(k + 24)$ $-$ $13 = 4(k - 13)$ which combines the information about $k$ from both of our original equations. Simplifying both sides of this equation, we get: $k + 11 = 4 k - 52$ Solving for $k$ , we get: $3 k = 63$ $k = 21$.